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Label Polynomial Discriminant Galois group Class group
8.2.4616192.1 x8 - 2x7 + 3x6 - 4x5 + 3x4 - 4x3 + 3x2 - 2x + 1 \( -\,2^{12}\cdot 7^{2}\cdot 23 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.8228864.1 x8 + 2x6 - 2x5 + 2x4 - 4x3 + 3x2 - 2x + 1 \( 2^{12}\cdot 7^{2}\cdot 41 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.8294400.1 x8 - 2x7 + x6 + 7x4 - 16x3 + 15x2 - 6x + 1 \( 2^{12}\cdot 3^{4}\cdot 5^{2} \) $Q_8:C_2$ (as 8T11) trivial
8.2.15167488.1 x8 - 2x7 + x6 + 4x5 - 7x4 + 4x3 + x2 - 2x + 1 \( -\,2^{12}\cdot 7\cdot 23^{2} \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.15429632.1 x8 - 2x7 + x6 + 2x3 - 2x2 + 1 \( -\,2^{12}\cdot 3767 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.18313216.1 x8 - 2x7 + x6 + x4 - 3x2 + 2x - 1 \( -\,2^{12}\cdot 17\cdot 263 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.20672512.1 x8 - 2x7 + 3x6 - 4x5 + 4x4 - 2x3 - 4x2 + 4x - 1 \( -\,2^{12}\cdot 7^{2}\cdot 103 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.21917696.1 x8 - 2x7 + 3x6 - 2x4 + 2x3 - 2x2 - 1 \( -\,2^{12}\cdot 5351 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.22974464.1 x8 - 2x7 + x6 - 4x4 + 6x3 - 6x2 + 4x - 1 \( 2^{12}\cdot 71\cdot 79 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.23040000.1 x8 - 2x7 - x6 - 5x4 - x2 - 2x + 1 \( 2^{12}\cdot 3^{2}\cdot 5^{4} \) $Q_8:C_2$ (as 8T11) trivial
8.2.23883776.1 x8 - 4x7 + 8x6 - 10x5 + 8x4 - 4x3 - x2 + 2x - 1 \( -\,2^{12}\cdot 7^{3}\cdot 17 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.25849856.1 x8 - x4 - 4x3 - 2x2 - 1 \( -\,2^{12}\cdot 6311 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.27496448.1 x8 - 2x7 + 3x6 - 4x5 + 8x4 - 10x3 + 8x2 - 4x + 1 \( 2^{12}\cdot 7^{2}\cdot 137 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.4.27496448.1 x8 - 2x7 - 3x6 + 8x5 + 2x4 - 10x3 + 4x - 1 \( 2^{12}\cdot 7^{2}\cdot 137 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.30306304.1 x8 - 4x7 + 8x6 - 10x5 + 6x4 - 3x2 + 2x - 1 \( -\,2^{12}\cdot 7^{2}\cdot 151 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.31092736.1 x8 - 2x7 - x6 + 5x4 - x2 - 2x - 1 \( -\,2^{12}\cdot 7591 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.33132544.1 x8 - 2x5 + 4x3 - x2 - 2x + 1 \( 2^{12}\cdot 8089 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.33517568.1 x8 - 2x7 - x6 + 4x5 + x4 - 4x3 - 3x2 + 6x - 1 \( -\,2^{12}\cdot 7^{2}\cdot 167 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.39809024.1 x8 - 2x7 - x6 + 4x5 - 2x4 - 2x3 + 4x2 - 4x + 1 \( -\,2^{12}\cdot 9719 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.39940096.1 x8 - 2x7 + x6 - 4x5 + 6x4 - 2x3 + 2x2 - 4x + 1 \( -\,2^{12}\cdot 7^{2}\cdot 199 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.40988672.1 x8 - 2x7 + x6 + x4 - 4x3 + 3x2 + 2x - 1 \( -\,2^{12}\cdot 10007 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.43552768.1 x8 - 2x7 + 5x6 - 4x5 + 7x4 - 4x3 + 5x2 - 2x + 1 \( 2^{12}\cdot 7^{3}\cdot 31 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.4.46370816.1 x8 - 4x5 + x4 + 4x3 - 4x2 + 1 \( 2^{12}\cdot 11321 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.46895104.1 x8 - 2x7 + x6 - 3x4 + x2 + 2x + 1 \( 2^{12}\cdot 107^{2} \) $S_4\times C_2$ (as 8T24) trivial
8.2.48197632.1 x8 - 2x7 + x6 - x4 + x2 - 2x + 1 \( -\,2^{12}\cdot 7\cdot 41^{2} \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.4.51089408.1 x8 - 2x6 + x4 - 4x3 + 4x - 1 \( 2^{12}\cdot 12473 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.53768192.1 x8 - 2x7 + 5x6 - 4x5 + 3x4 - x2 - 2x + 1 \( -\,2^{12}\cdot 13127 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.56004608.1 x8 - 2x7 + 3x6 - 4x5 - x4 - x2 + 2x + 1 \( 2^{12}\cdot 11^{2}\cdot 113 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.56070144.4 x8 + 8x4 + 24x2 + 16 \( 2^{12}\cdot 3^{4}\cdot 13^{2} \) $D_4\times C_2$ (as 8T9) trivial
8.2.57110528.1 x8 - 2x7 + 3x6 - 4x5 + 4x4 - 2x3 + 2x2 - 1 \( -\,2^{12}\cdot 73\cdot 191 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.62820352.1 x8 - 2x7 - 3x6 + 4x5 + 5x4 - 4x3 - 3x2 + 2x + 1 \( 2^{12}\cdot 7^{2}\cdot 313 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.64000000.2 x8 + 2x6 + 4x4 + 8x2 + 16 \( 2^{12}\cdot 5^{6} \) $C_4\times C_2$ (as 8T2) trivial
8.4.65507328.1 x8 - 4x6 - 2x5 + 4x4 + 4x3 + x2 - 2x - 1 \( 2^{12}\cdot 3^{2}\cdot 1777 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.66031616.1 x8 - 2x7 + 3x6 - 8x5 + 8x4 - 2x3 - 2x2 + 4x - 1 \( 2^{12}\cdot 7^{3}\cdot 47 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.4.68128768.1 x8 - 2x7 - x6 + 3x4 + 4x3 - 3x2 - 2x + 1 \( 2^{12}\cdot 16633 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.71995392.1 x8 - 4x7 + 4x6 + 2x5 - 8x3 + 7x2 - 2x + 1 \( 2^{12}\cdot 3^{4}\cdot 7\cdot 31 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial
8.0.71995392.2 x8 - 2x7 + 3x6 - 4x5 - 4x4 + 2x3 + 6x2 + 4x + 1 \( 2^{12}\cdot 3^{4}\cdot 7\cdot 31 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial
8.2.72052736.1 x8 - 4x7 + 4x6 + 2x5 - 4x4 + 3x2 - 2x - 1 \( -\,2^{12}\cdot 7^{2}\cdot 359 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.73691136.1 x8 - 2x7 + 5x6 - 4x5 + 3x4 + 4x3 - 5x2 + 6x - 1 \( -\,2^{12}\cdot 3^{2}\cdot 1999 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.74215424.1 x8 - 2x6 - 2x5 + 2x4 + 4x3 - x2 - 2x - 1 \( -\,2^{12}\cdot 18119 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.78344192.1 x8 - 2x7 + x6 - x4 + 4x3 - 3x2 + 2x - 1 \( -\,2^{12}\cdot 31\cdot 617 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.78475264.1 x8 - 4x7 + 4x6 + 2x5 - 6x4 + 4x3 + x2 - 2x - 1 \( -\,2^{12}\cdot 7^{2}\cdot 17\cdot 23 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.78475264.2 x8 - 2x7 + 3x6 - 4x5 - 2x4 - 2x3 + 12x2 - 8x + 1 \( -\,2^{12}\cdot 7^{2}\cdot 17\cdot 23 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.79654912.1 x8 - 2x7 + x6 - x4 + 4x3 - 5x2 + 2x - 1 \( -\,2^{12}\cdot 19447 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.82087936.1 x8 - 4x7 + 4x6 + 2x5 - 4x4 - x2 + 2x + 1 \( 2^{12}\cdot 7^{2}\cdot 409 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.4.83136512.1 x8 - 2x6 - 2x5 + 4x3 - x2 - 2x + 1 \( 2^{12}\cdot 20297 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.85430272.1 x8 - 2x7 - x6 + 4x4 + 2x3 - 2x2 - 1 \( 2^{12}\cdot 20857 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.86413312.1 x8 - 2x6 - 3x4 - 4x3 - 4x2 - 4x - 1 \( 2^{12}\cdot 17^{2}\cdot 73 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.87912448.1 x8 - 2x5 - 4x3 - 5x2 - 6x - 1 \( -\,2^{12}\cdot 13^{2}\cdot 127 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.91983872.1 x8 - 2x7 - x6 + 4x5 - x4 + x2 - 2x - 1 \( 2^{12}\cdot 17\cdot 1321 \) $S_4\wr C_2$ (as 8T47) trivial
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